James buys 12 toys and labels each with the same selling price.

2112 or any other really does not change the question.

Let the labeled price be x.
So 8 sold at 0.8x => 6.4x
4 sold at 0.8x*\(\frac{75}{100}\) or 0.6x => 2.4x
Total = 6.4x+2.4x=8.8x

If there is a 10% profit and actual price be y for all 12 toys, then \(\frac{110}{100}y=8.8x…………..y=8x\)
Also, actual labeled price = 12*x

Profit = 12x-8x = 4x

Profit % = \(\frac{4x}{8x}*100=50\)


B
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Labelled Price of each toy= x

for first 8 toys= 0.8x
Remaininng 4= 0.75*0.8 =0.6 x

Selling Price (Total) =8*.8x +4*.6x = 8.8x =2112

x=240 (calculation actually not required)

Given, Profit =10% and let cost price for each toy be y

1.1*12y = 8.8x
12y (C.P)= 8x

if all toys were to be sold at non discounted Price , S.p= 12 x

Would be Profit = 12x-8x = 4x

Profit %= (4x/8x)*100
=50%

Solution:

Let us assume the MP of each toy \(= x\). So MP for all (12) toys \(= 12x\).

For first \(8\) toys, selling price \(SP= 8x(1-\frac{20}{100})=8x\times 0.8=6.4x\) Because we know the formula \(SP=MP(1+\frac{d}{100})\)


and for rest \(4\) toys, selling price \(SP= 4x(1-\frac{20}{100})(1-\frac{25}{100})=4x\times 0.8\times 0.75=2.4x\) Because we know the formula \(SP=MP(1+\frac{d_1}{100})(1+\frac{d_2}{100})\)


So the total \(SP_T = 6.4x+2.4x=8.8x\).

Let us assume the total cost price of these \(12\) toys \(= y\).

We are told that he makes a \(10\)% profit.

This means we can write \(8.8x=y(1+\frac{10}{100})⇒y=8x\). Because we know the formula \(SP=CP(1+\frac{p}{100})\)

So, total \(CP_T=8x\) and without discount, total \(SP_T = 12x\).

Profit \(= 12x-8x=4x\). And profit % \(= \frac{4x}{8x}\times 100=50\)%.

HEnce the right answer is Option B.
_________________

Let CP = x

SP= y

8(0.8y) + 4(0.6y) = 2112

6.4y + 2.4y = 2112

8.8y = 2112

y = 240.


2112-12x/12x X 100 = 10

211200-1200x = 120x

1320x = 211200

x = 160.

Therefore

960/1920 X 100 = 50%

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